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      SUBROUTINE <a name="CHEGV.1"></a><a href="chegv.f.html#CHEGV.1">CHEGV</a>( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
     $                  LWORK, RWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               RWORK( * ), W( * )
      COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CHEGV.20"></a><a href="chegv.f.html#CHEGV.1">CHEGV</a> computes all the eigenvalues, and optionally, the eigenvectors
</span><span class="comment">*</span><span class="comment">  of a complex generalized Hermitian-definite eigenproblem, of the form
</span><span class="comment">*</span><span class="comment">  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
</span><span class="comment">*</span><span class="comment">  Here A and B are assumed to be Hermitian and B is also
</span><span class="comment">*</span><span class="comment">  positive definite.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ITYPE   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          Specifies the problem type to be solved:
</span><span class="comment">*</span><span class="comment">          = 1:  A*x = (lambda)*B*x
</span><span class="comment">*</span><span class="comment">          = 2:  A*B*x = (lambda)*x
</span><span class="comment">*</span><span class="comment">          = 3:  B*A*x = (lambda)*x
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOBZ    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  Compute eigenvalues only;
</span><span class="comment">*</span><span class="comment">          = 'V':  Compute eigenvalues and eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangles of A and B are stored;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangles of A and B are stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrices A and B.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) COMPLEX array, dimension (LDA, N)
</span><span class="comment">*</span><span class="comment">          On entry, the Hermitian matrix A.  If UPLO = 'U', the
</span><span class="comment">*</span><span class="comment">          leading N-by-N upper triangular part of A contains the
</span><span class="comment">*</span><span class="comment">          upper triangular part of the matrix A.  If UPLO = 'L',
</span><span class="comment">*</span><span class="comment">          the leading N-by-N lower triangular part of A contains
</span><span class="comment">*</span><span class="comment">          the lower triangular part of the matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
</span><span class="comment">*</span><span class="comment">          matrix Z of eigenvectors.  The eigenvectors are normalized
</span><span class="comment">*</span><span class="comment">          as follows:
</span><span class="comment">*</span><span class="comment">          if ITYPE = 1 or 2, Z**H*B*Z = I;
</span><span class="comment">*</span><span class="comment">          if ITYPE = 3, Z**H*inv(B)*Z = I.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
</span><span class="comment">*</span><span class="comment">          or the lower triangle (if UPLO='L') of A, including the
</span><span class="comment">*</span><span class="comment">          diagonal, is destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX array, dimension (LDB, N)
</span><span class="comment">*</span><span class="comment">          On entry, the Hermitian positive definite matrix B.
</span><span class="comment">*</span><span class="comment">          If UPLO = 'U', the leading N-by-N upper triangular part of B
</span><span class="comment">*</span><span class="comment">          contains the upper triangular part of the matrix B.
</span><span class="comment">*</span><span class="comment">          If UPLO = 'L', the leading N-by-N lower triangular part of B
</span><span class="comment">*</span><span class="comment">          contains the lower triangular part of the matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, if INFO &lt;= N, the part of B containing the matrix is
</span><span class="comment">*</span><span class="comment">          overwritten by the triangular factor U or L from the Cholesky
</span><span class="comment">*</span><span class="comment">          factorization B = U**H*U or B = L*L**H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  W       (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          If INFO = 0, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The length of the array WORK.  LWORK &gt;= max(1,2*N-1).
</span><span class="comment">*</span><span class="comment">          For optimal efficiency, LWORK &gt;= (NB+1)*N,
</span><span class="comment">*</span><span class="comment">          where NB is the blocksize for <a name="CHETRD.88"></a><a href="chetrd.f.html#CHETRD.1">CHETRD</a> returned by <a name="ILAENV.88"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.93"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) REAL array, dimension (max(1, 3*N-2))
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  <a name="CPOTRF.100"></a><a href="cpotrf.f.html#CPOTRF.1">CPOTRF</a> or <a name="CHEEV.100"></a><a href="cheev.f.html#CHEEV.1">CHEEV</a> returned an error code:
</span><span class="comment">*</span><span class="comment">             &lt;= N:  if INFO = i, <a name="CHEEV.101"></a><a href="cheev.f.html#CHEEV.1">CHEEV</a> failed to converge;
</span><span class="comment">*</span><span class="comment">                    i off-diagonal elements of an intermediate
</span><span class="comment">*</span><span class="comment">                    tridiagonal form did not converge to zero;
</span><span class="comment">*</span><span class="comment">             &gt; N:   if INFO = N + i, for 1 &lt;= i &lt;= N, then the leading
</span><span class="comment">*</span><span class="comment">                    minor of order i of B is not positive definite.
</span><span class="comment">*</span><span class="comment">                    The factorization of B could not be completed and
</span><span class="comment">*</span><span class="comment">                    no eigenvalues or eigenvectors were computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      COMPLEX            ONE
      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LQUERY, UPPER, WANTZ
      CHARACTER          TRANS
      INTEGER            LWKOPT, NB, NEIG
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.121"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.122"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
      EXTERNAL           <a name="ILAENV.123"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>, <a name="LSAME.123"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CHEEV.126"></a><a href="cheev.f.html#CHEEV.1">CHEEV</a>, <a name="CHEGST.126"></a><a href="chegst.f.html#CHEGST.1">CHEGST</a>, <a name="CPOTRF.126"></a><a href="cpotrf.f.html#CPOTRF.1">CPOTRF</a>, CTRMM, CTRSM, <a name="XERBLA.126"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      WANTZ = <a name="LSAME.135"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'V'</span> )
      UPPER = <a name="LSAME.136"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      LQUERY = ( LWORK.EQ. -1 )
<span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
         INFO = -1
      ELSE IF( .NOT.( WANTZ .OR. <a name="LSAME.142"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'N'</span> ) ) ) THEN
         INFO = -2
      ELSE IF( .NOT.( UPPER .OR. <a name="LSAME.144"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -6
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         NB = <a name="ILAENV.155"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="CHETRD.155"></a><a href="chetrd.f.html#CHETRD.1">CHETRD</a>'</span>, UPLO, N, -1, -1, -1 )
         LWKOPT = MAX( 1, ( NB + 1 )*N )
         WORK( 1 ) = LWKOPT
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY ) THEN
            INFO = -11
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.165"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CHEGV.165"></a><a href="chegv.f.html#CHEGV.1">CHEGV</a> '</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Form a Cholesky factorization of B.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="CPOTRF.178"></a><a href="cpotrf.f.html#CPOTRF.1">CPOTRF</a>( UPLO, N, B, LDB, INFO )
      IF( INFO.NE.0 ) THEN
         INFO = N + INFO
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Transform problem to standard eigenvalue problem and solve.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="CHEGST.186"></a><a href="chegst.f.html#CHEGST.1">CHEGST</a>( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
      CALL <a name="CHEEV.187"></a><a href="cheev.f.html#CHEEV.1">CHEEV</a>( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
<span class="comment">*</span><span class="comment">
</span>      IF( WANTZ ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Backtransform eigenvectors to the original problem.
</span><span class="comment">*</span><span class="comment">
</span>         NEIG = N
         IF( INFO.GT.0 )
     $      NEIG = INFO - 1
         IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
</span><span class="comment">*</span><span class="comment">           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
</span><span class="comment">*</span><span class="comment">
</span>            IF( UPPER ) THEN
               TRANS = <span class="string">'N'</span>
            ELSE
               TRANS = <span class="string">'C'</span>
            END IF
<span class="comment">*</span><span class="comment">
</span>            CALL CTRSM( <span class="string">'Left'</span>, UPLO, TRANS, <span class="string">'Non-unit'</span>, N, NEIG, ONE,
     $                  B, LDB, A, LDA )
<span class="comment">*</span><span class="comment">
</span>         ELSE IF( ITYPE.EQ.3 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           For B*A*x=(lambda)*x;
</span><span class="comment">*</span><span class="comment">           backtransform eigenvectors: x = L*y or U'*y
</span><span class="comment">*</span><span class="comment">
</span>            IF( UPPER ) THEN
               TRANS = <span class="string">'C'</span>
            ELSE
               TRANS = <span class="string">'N'</span>
            END IF
<span class="comment">*</span><span class="comment">
</span>            CALL CTRMM( <span class="string">'Left'</span>, UPLO, TRANS, <span class="string">'Non-unit'</span>, N, NEIG, ONE,
     $                  B, LDB, A, LDA )
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      WORK( 1 ) = LWKOPT
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CHEGV.230"></a><a href="chegv.f.html#CHEGV.1">CHEGV</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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